Piecewise Functions

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas for different intervals of its domain.

Front

How do you evaluate a piecewise function at a specific point?

Back

To evaluate a piecewise function at a specific point, determine which interval the point falls into and then use the corresponding expression to find the function's value.

Front

What does the notation f(x) = { expression1 if condition1; expression2 if condition2; ... } represent?

Back

This notation represents a piecewise function where each expression is used based on the condition that is satisfied by the input x.

Front

How can you determine the number of pieces in a piecewise function?

Back

The number of pieces in a piecewise function is determined by the number of different expressions or formulas defined for different intervals of the domain.

Front

What is the significance of the domain in piecewise functions?

Back

The domain of a piecewise function specifies the input values for which each piece of the function is valid.

Front

How do you graph a piecewise function?

Back

To graph a piecewise function, plot each piece of the function according to its defined interval, ensuring to use open or closed circles to indicate whether endpoints are included.

Front

What is the value of f(-2) if f(x) = { 2x + 4 if x < 0; x^2 if x >= 0 }?

Back

f(-2) = 2(-2) + 4 = 0.

Front

How do you match a graph to its corresponding piecewise function?

Back

To match a graph to its corresponding piecewise function, analyze the behavior of the graph in different intervals and identify the equations that describe those behaviors.

Front

What is the value of f(0) if f(x) = { x + 1 if x < 0; 1 if x = 0; x^2 if x > 0 }?

Back

f(0) = 1.

Front

What is the formula for a piecewise function that is defined as f(x) = { -x + 1 if x < 4; x if x >= 4 }?

Back

The formula is f(x) = { -x + 1 for x < 4; x for x >= 4 }.